Let $k$ be a field and $X$ a $k$-scheme. We say that $X$ is **geometrically connected** if the scheme $X_{k'}$ is connected for every field extension $k'$ of $k$.

Let $k^{\mathrm{sep}}$ be the separable closure of $k$. Then $X$ is geometrically connected if and only if the base change $X_{k^{\mathrm{sep}}}$ is connected.

category: algebraic geometry

Last revised on July 22, 2024 at 07:28:07. See the history of this page for a list of all contributions to it.